Winning at roulette. Roulette is a very popular game in many American casinos. In Roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2,c, 35, 36. The number of the arc on which the ball stops is the outcome of one play of the game. The numbers are also colored in the manner shown in the following table.

Red: 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 Black: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 Green: 00, 0 Players may place bets on the table in a variety of ways, including bets on odd, even, red, black, high, low, etc. Consider the following events:

A: 5The outcome is an odd number 100 and 0 are considered neither odd nor even.26 B: 5The outcome is a black number.6 C: 5The outcome is a low number 11-182.6

a. Define the event A ¨ B as a specific set of sample points.

b. Define the event A ∪ B as a specific set of sample points.

c. Find P1A2, P1B2, P1A ¨ B2, P1A ∪ B2, and P(C) by summing the probabilities of the appropriate sample points.

d. Define the event A ¨ B ¨ C as a specific set of sample points.

e. Use the additive rule to find P1A ∪ B2. Are events A and B mutually exclusive? Why?

f. Find P1A ¨ B ¨ C2 by summing the probabilities of the sample points given in part d.

g. Define the event 1A ∪ B ∪ C2 as a specific set of sample points.

h. Find P1A ∪ B ∪ C2 by summing the probabilities of the sample points given in part g.